Results 1  10
of
15
Innocent Statements and Their Metaphysically Loaded Counterparts
, 2007
"... here is an old puzzle about ontology, one that has been puzzling enough to cast a shadow of doubt over the legitimacy of ontology as a philosophical project. The puzzle concerns in particular ontological questions about natural numbers, properties, and propositions, but also some other things as wel ..."
Abstract

Cited by 8 (4 self)
 Add to MetaCart
here is an old puzzle about ontology, one that has been puzzling enough to cast a shadow of doubt over the legitimacy of ontology as a philosophical project. The puzzle concerns in particular ontological questions about natural numbers, properties, and propositions, but also some other things as well. It arises as follows: ontological questions about numbers, properties, or propositions are questions about whether reality contains such entities, whether they are part of the stuff that the world is made of. The ontological questions about numbers, properties, or propositions thus seem to be substantive metaphysical questions about what is part of reality. Complicated as these questions may be, they can nonetheless be stated simply in ordinary English with the words ‘Are there numbers/properties/propositions?’ However, it seems that such a question can be answered quite immediately in the affirmative. It seems that there are trivial arguments that have the conclusion that there are numbers/properties/
Logicism Reconsidered
 In Shapiro
, 2005
"... This paper is divided into four sections. The first two identify different logicist theses, and show that their truthvalues can be conclusively established on minimal assumptions. Section 3 sets forth a notion of ‘contentrecarving ’ as a possible constraint on logicist theses. Section 4—which is l ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
This paper is divided into four sections. The first two identify different logicist theses, and show that their truthvalues can be conclusively established on minimal assumptions. Section 3 sets forth a notion of ‘contentrecarving ’ as a possible constraint on logicist theses. Section 4—which is largely independent from the rest of the paper—is a discussion of ‘NeoLogicism’. 1 Logicism 1.1 What is Logicism? Briefly, logicism is the view that mathematics is a part of logic. But this formulation is imprecise because it fails to distinguish between the following three claims: 1. LanguageLogicism The language of mathematics consists of purely logical expressions.
THE RELIABILITY CHALLENGE AND THE EPISTEMOLOGY OF LOGIC
"... This paper concerns a problem in the epistemology of logic. This problem is an analogue of the BenacerrafField problem for mathematical Platonism. It is also an analogue of ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
This paper concerns a problem in the epistemology of logic. This problem is an analogue of the BenacerrafField problem for mathematical Platonism. It is also an analogue of
The Mathematician as a Formalist
 in Truth in Mathematics (H.G. Dales and
, 1998
"... Introduction The existence of this meeting bears testimony to the anodyne remark that there is a continuing debate about what it means to say of a statement in mathematics that it is `true'. This debate began at least 2500 years ago, and will presumably continue at least well into the next mil ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Introduction The existence of this meeting bears testimony to the anodyne remark that there is a continuing debate about what it means to say of a statement in mathematics that it is `true'. This debate began at least 2500 years ago, and will presumably continue at least well into the next millennium; it would be implausible and perhaps presumptuous to suppose that even the union of the talented and distinguished speakers that have been assembled here in Mussomeli will approach any solution to the problem, or even arrive at a consensus of what a solution would amount to. In the end, it falls to the philosophers, with their professional expertise and training, to carry forward the debate and to move us to a fuller understanding of this subtle and elusive matter. Indeed, we are hearing at this meeting a variety of contributions to the debate from different philosophical points of view; also, there is a good number of recent published contributions to the debate (see (Maddy 1990)
Models and recursivity
, 2002
"... It is commonly held that the natural numbers sequence 0, 1, 2,... possesses a unique structure. Yet by a well known model theoretic argument, there exist nonstandard models of the formal theory which is generally taken to axiomatize all of our practices and intentions pertaining to use of the term ..."
Abstract
 Add to MetaCart
(Show Context)
It is commonly held that the natural numbers sequence 0, 1, 2,... possesses a unique structure. Yet by a well known model theoretic argument, there exist nonstandard models of the formal theory which is generally taken to axiomatize all of our practices and intentions pertaining to use of the term “natural number. ” Despite the structural similarity of this argument to the influential set theoretic indeterminacy argument based on the downward LöwenheimSkolem theorem, most theorists agree that the number theoretic version does not have skeptical consequences about the reference of “natural number ” analogous to the ‘relativity ’ Skolem claimed pertains to notions such as “uncountable ” and “cardinal. ” In this paper I argue that recent proposals by Shapiro, Lavine, McGee and Field which aim to distinguish the number and set theoretic indeterminacy arguments by locating extramathematical constraints on the interpretation of our number theoretic vocabulary are inadequate. I then suggest that if we
A Puzzle for Structuralism
, 2003
"... Structuralism is the view that the subjectmatter of a theory of pure mathematics is a mathematical structure. Different versions of structuralism tell different stories about what mathematical structures are.1 But assuming that they agree about when a model2 exemplifies a mathematical structure, t ..."
Abstract
 Add to MetaCart
(Show Context)
Structuralism is the view that the subjectmatter of a theory of pure mathematics is a mathematical structure. Different versions of structuralism tell different stories about what mathematical structures are.1 But assuming that they agree about when a model2 exemplifies a mathematical structure, they can agree about the conditions under which a sentence of pure mathematics is true:
Existence, Truth, and Method In the Mathematical Theory of Sets _______________________________
, 2000
"... In these three chapters I treat a variety of issues that surround the current state of set theory. Through an analysis of the relationships between set theory and other branches of mathematics, I try to paint a truer picture of the nature of the theory of sets than what seems to be the prevalent cha ..."
Abstract
 Add to MetaCart
In these three chapters I treat a variety of issues that surround the current state of set theory. Through an analysis of the relationships between set theory and other branches of mathematics, I try to paint a truer picture of the nature of the theory of sets than what seems to be the prevalent characterization of the subject. This same analysis directs my approach to questions about certain undecidable statements in set theory. My aim is to suggest that a proper understanding of set theory should provoke a realist attitude toward mathematical truth. One consequence of having such an attitude is that the present formal structure of set theory necessarily fails to capture all that there is to know about sets. With that in mind, I propose a change in the foundations of the theory which I hope is a beginning of a richer set theory. This volume was written under the generous support of the Rice Undergraduate Scholars ’ Program in 1999 and 2000. I thank Professors James Kinsey, Scott Derrick, and Don Johnson for their enthusiasm and the opportunities offered in the program. Thanks are also due to Byeong UkYi and Alasdair Urquhart, whose insights and encouragement greatly affected the direction of my research. Professor Richard Grandy of the Rice University Philosophy Department was my advisor during the course of this research. I am greatly indebted to his contributions in this project.
unknown title
"... 100 agustín rayo perceptual experience. In perception, the world acts on us, and we act right back. 7 ..."
Abstract
 Add to MetaCart
(Show Context)
100 agustín rayo perceptual experience. In perception, the world acts on us, and we act right back. 7